Question

The maximum velocity divided by the average velocityin laminar poisseuille flow between two parallel plates is

Answer 1

and velocity of laminar flow

garala brijesh   -Posted on 25 Apr 16
Good

Pankaj   -Posted on 29 Sep 15
• The equation of velocity distribution of laminar fluid flow through a pipe having radius R is given by,

u = – (1 / (4 μ)) (∂p/∂x) [R2 – r2]

where,
u = velocity of fluid
R = radius of pipe
r = distance from the centre of the pipe

• Maximum velocity occurs at the centre where r = 0. Putting this in above equation,

Umax = – (1 / (4 μ)) (∂p/∂x) [R2]

• Average velocity obtained by dividing discharge of the fluid across the cross sectional area of pipe (πR2)

dQ = Velocity at radus r x Area of ring element 

= u x 2πr dr

= – (1 / (4 μ)) (∂p/∂x) [R2] x 2πr dr

• Therefore,

Q = 0∫R – (1 / (4 μ)) (∂p/∂x) [R2] x 2πr dr

= (π/8μ) (- ∂p/∂x) R4

• Therefore, Average velocity,

u = Q/A

u = (1/8μ) (- ∂p/∂x) R2

• Ratio of maximum and average velocity 

Umax / u = 2